Bias away from the null due to miscounted outcomes? A case study on the TORCH trial

Count outcomes occur in virtually all disciplines, such as medicine, epidemiology or biology, but they often contain error. Recently, it has been shown that self-reported numbers of exacerbations of Chronic Obstructive Pulmonary Disease patients can be considerably miscounted. Motivated by this result, we reanalysed data from the Towards a Revolution in Chronic Obstructive Pulmonary Disease Health trial, a large randomized controlled trial with the self-reported number of exacerbations of Chronic Obstructive Pulmonary Disease patients as outcome. To adjust for miscounting error in the response of Poisson and (zero-inflated) negative binomial models, we introduce novel, general methodology. The key idea is to formulate a zero-inflated negative binomial model to capture the error mechanism. This parametric approach automatically circumvents drawbacks of previously suggested methodology that treats miscounted outcomes in the misclassification framework. Prior information for the response error model parameters was elicited from validation data of an external study and adaptively weighted to account for potential prior-data conflict. The results of the Bayesian hierarchical modelling approach indicated that the treatment effect has been overestimated in the original study. However, closer inspection revealed that this unexpected result was an artefact of an unaccounted time dependency of the treatment effect.